On metric equivalence of the Brieskorn-Pham hypersurfaces

Abstract

We show that two bi-Lipschitz equivalent Brieskorn-Pham hypersurfaces have the same multiplicities at $0$. Moreover we show that if two algebraic $(n-1)$-dimensional cones $P,R\subset {\mathbb{C}}^n$ with isolated singularities are homeomorphic, then they have the same degree.

5 pages